The expected number of symmetries in locally restricted trees II

Abstract

Asymptotic formulas are derived for the number of symmetries in several types of unlabeled trees with vertices of restricted degree. The trees are d-trees whose vertices have degree at most d and (1, d)-trees whose vertices have degree 1 or d. These results together with similar results for the number of such trees provide asymptotic formulas for the expected number of symmetries in these trees.